Question

What is the simplest form of

Answer 1

The simplest form of
`\sqrt[3]{27a^(3)b^(7)}` is

3ab²(∛b)

Explanation:

The given term is:

`\sqrt[3]{27a^(3)b^(7)}`

To convert it into its simplest form, we will apply simple mathematical rules to simplify the power of individual terms.

`\sqrt[3]{27a^(3)b^(7)}\\= \sqrt[3]{3^(3) a^(3)b^(7)}\\= \sqrt[3]{3^(3)a^(3)b^(6)b}\\= 3^(3/3) a^(3/3)b^(6/3)b^(1/3)}\\= 3ab^(2)(\sqrt[3]{b})`

While simplifying the term, we basically took the cube root of individual terms. The powers cancelled out cube root for some terms. In the end, we were left with the simplest form of the expression.